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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E17">Th18</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: PENCIL_3:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">A</font> being   <a href="pencil_1.html#V14" title="PENCIL_1:attr.14">PLS-yielding</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b1">I</font><br/>  for <font color="Olive" title="b3">b</font> being   non  <a href="pencil_1.html#V12" title="PENCIL_1:attr.12">trivial-yielding</a>   <a href="pencil_1.html#V15" title="PENCIL_1:attr.15">Segre-like</a>   <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedSubset</a> of  <a href="pralg_1.html#K14" title="PRALG_1:func.14">Carrier</a> <font color="Olive" title="b2">A</font><br/>  for <font color="Olive" title="b4">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="pencil_1.html#K2" title="PENCIL_1:func.2">.</a> <span class="p2">(<span class="default"><a href="pencil_1.html#K3" title="PENCIL_1:func.3">indx</a> <font color="Olive" title="b3">b</font></span>)</span></span>)</span>  ex <font color="Olive" title="b5">p</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b1">I</font> st <br/>( <font color="Olive" title="b5">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Olive" title="b3">b</font> &amp; <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">p</font> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</a> (<span class="p3">(<span class="default"><a href="pencil_1.html#K3" title="PENCIL_1:func.3">indx</a> <font color="Olive" title="b3">b</font></span>)</span>,<font color="Olive" title="b4">x</font>)</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">b</font> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</a> (<span class="p2">(<span class="default"><a href="pencil_1.html#K3" title="PENCIL_1:func.3">indx</a> <font color="Olive" title="b3">b</font></span>)</span>,<span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b4">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>)</span>)</span> )</div></div>
